A CLASS OF SIS EPIDEMIC MODEL WITH SATURATION INCIDENCE AND AGE OF INFECTION

Saturating contact rate of individual contacts is crucial in an epidemiology model. A mathematical SIR model with saturation incidence and age of infection is formulated in this paper. In addition, we study the dynamical behavior of this model and define the basic reproductive number R0. The authors also prove that the diseased-free equilibrium is globally asymptotically stable if R0 〈 1. The endemic equilibrium is locally asymptotically stable if K1 〉 α and R0 〉 1.

The Influence of Saturated and Bilinear Incidence Functions on the Dynamical Behavior of HIV Model Using Galerkin Scheme Having a Polynomial of Order Two

Mathematical modelling has been extensively used to measure intervention strategies for the control of contagious conditions.Alignment between different models is pivotal for furnishing strong substantiation for policymakers because the differences in model features can impact their prognostications.Mathematical modelling has been widely used in order to better understand the transmission,treatment,and prevention of infectious diseases.Herein,we study the dynamics of a human immunodeficiency virus(HIV)infection model with four variables:S(t),I(t),C(t),and A(t)the susceptible individuals;HIV infected individuals(with no clinical symptoms of AIDS);HIV infected individuals(under ART with a viral load remaining low),and HIV infected individuals with two different incidence functions(bilinear and saturated incidence functions).A novel numerical scheme called the continuous Galerkin-Petrov method is implemented for the solution of themodel.The influence of different clinical parameters on the dynamical behavior of S(t),I(t),C(t)and A(t)is described and analyzed.All the results are depicted graphically.On the other hand,we explore the time-dependent movement of nanofluid in porous media on an extending sheet under the influence of thermal radiation,heat flux,hall impact,variable heat source,and nanomaterial.The flow is considered to be 2D,boundary layer,viscous,incompressible,laminar,and unsteady.Sufficient transformations turn governing connected PDEs intoODEs,which are solved using the proposed scheme.To justify the envisaged problem,a comparison of the current work with previous literature is presented.

Stability Analysis of SIQS Epidemic Model with Saturated Incidence Rate

A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium exists when the basic reproduction number R0, is less or greater than unity respectively. The global stability of the disease-free and endemic equilibrium is proved using Lyapunov functions and Poincare-Bendixson theorem plus Dulac’s criterion respectively.

Bifurcation analysis of an SIS epidemic model with a generalized non-monotonic and saturated incidence rate

In this paper,a new generalized non-monotonic and saturated incidence rate was introduced into a susceptible-infected-susceptible(SIS)epidemic model to account for inhibitory effect and crowding effect.The dynamic properties of the model were studied by qualitative theory and bifurcation theory.It is shown that when the infuence of psychological factors is large,the model has only disease-free equilibrium point,and this disease-free equilibrium point is globally asymptotically stable;when the influence of psychological factors is small,for some parameter conditions,the model has a unique endemic equilibrium point,which is a cusp point of co-dimension two,and for other parameter conditions the model has two endemic equilibrium points,one of which could be weak focus or center.In addition,the results of the model undergoing saddle-node bifurcation,Hopf bifurcation and Bogdanov-Takens bifurcation as the parameters vary were also proved.These results shed light on the impact of psychological behavior of susceptible people on the disease transmission.

A regime-switching stochastic SIR epidemic model with a saturated incidence and limited medical resources

The stochastic switching SIR epidemic model with saturated incidence and limited medical treatment is investigated in this paper.By using Lyapunov methods and Ito formula,we first prove that the system has a unique global positive solution with any positive initial value.Then combining inequality technique and the ergodic property of Markov switching,the suficient conditions for extinction and persistence in the mean of the disease are established.The results demonstrate that increasing medical resources and improving supply efficiency can accelerate the transition from the persistent state to the extinct state.Meanwhile,the high incidence rate will slow down the extinction of the disease.Specially,the switching noise can induce the system to toggle between the extinct and persistent states.Finally,some numerical simulations are carried out to confirm the analytical results.

STABILITY ANALYSIS OF A DELAYED SIRS EPIDEMIC MODEL WITH VACCINATION AND NONLINEAR INCIDENCE

In this paper, an SIRS epidemic model with time delay and vaccination is investigated. By analyzing the corresponding characteristic equation, the local stability of diseasefree equilibrium of the model is established. By constructing Lyapunov functional, sufficient conditions are established for the local stability of an endemic equilibrium of the model. Further, a threshold value is obtained. By using comparison arguments, it is proved when the threshold value is less than unity, the diseasefree equilibrium is globally asymptoti cally stable. When the threshold value is greater than unity, by using an iteration scheme and by constructing appropriate Lyapunov functional, respectively, sufficient conditions are derived for the global stability of the endemic equilibrium of the model. Numerical simulations are carried out to illustrate the theoretical results.

Analysis of SVEIR worm attack model with saturated incidence and partial immunization

Internet worms can propagate across networks at terrifying speeds,reduce network security to a remarkable extent,and cause heavy economic losses.Thus,the rapid elimination of Internet worms using partial immunization becomes a significant matter for sustaining Internet infrastructure.This paper addresses this issue by presenting a novel worm susceptible-vaccinated-exposed-infectious-recovered model,named the SVEIR model.The SVEIR model extends the classical susceptible-exposed-infectious-recovered model(refer to SEIR model)through incorporating a saturated incidence rate and a partial immunization rate.The basic reproduction number in the SVEIR model is obtained.By virtue of the basic reproduction number,we prove the global stabilities of an infection-free equilibrium point and a unique endemic equilibrium point.Numerical methods are used to verify the proposed SVEIR model.Simulation results show that partial immunization is highly effective for eliminating worms,and the SVEIR model is viable for controlling and forecasting Internet worms.

Dynamical behavior of a stochastic multigroup staged-progression HIV model with saturated incidence rate and higher-order perturbations

In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqueness of an ergodic stationary distribu-tion of positive solutions to the system by establishing a suitable stochastic Lyapunovfunction.In addition,we make up adequate conditions for complete eradication and wip-ing out the infectious disease.In a biological interpretation,the existence of a stationarydistribution implies that the disease will prevail and persist in the long term.Finally,examples and numerical simulations are introduced to validate our theoretical results.